Method and system for object reconstruction

ABSTRACT

A system and method are presented for use in the object reconstruction. The system comprises an illuminating unit, and an imaging unit (see FIG.  1 ). The illuminating unit comprises a coherent light source and a generator of a random speckle pattern accommodated in the optical path of illuminating light propagating from the light source towards an object, thereby projecting onto the object a coherent random speckle pattern. The imaging unit is configured for detecting a light response of an illuminated region and generating image data. The image data is indicative of the object with the projected speckles pattern and thus indicative of a shift of the pattern in the image of the object relative to a reference image of said pattern. This enables real-time reconstruction of a three-dimensional map of the object.

REFERENCE TO CROSS-RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/763,738, filed Feb. 11, 2013, which is a continuation of U.S. patentSer. No. 11/991,994 (now U.S. Pat. No. 8,400,494), filed Mar. 25, 2010,in the national phase of PCT Patent Application PCT/IL2006/000335, filedMar. 14, 2006, which claims priority from U.S. provisional applicationNo. 60/724,903, filed Oct. 11, 2005, herein incorporated by reference inits entirety.

FIELD OF THE INVENTION

This invention relates to a method and system for object reconstruction,enabling to extract highly resolved and real-time 3-D information.

REFERENCES

The following references are considered to be pertinent for the purposeof understanding the background of the present invention:

-   1. S. Avidan and A. Shashua, “Trajectory triangulation: 3D    reconstruction of moving points from amonocular image sequence,”    PAMI, 22, 348-357 (2000).-   2. Y. G. Leclerc and A. F. Bobick, “The direct computation of height    from shading,” CVPR, 552-558 (1991).-   3. R. Zhang and M. Shah, “Shape from intensity gradient,” SMC-A, 29,    318 (1999).-   4. R. Zhang and M. Shah, “Height recovery from intensity gradients,”    CVPR, 508-513 (1994).-   5. B. K. P. Horn, “Height and gradient from shading,” IJCV, 5, 37-76    (1990).-   6. A. M. Bruckstein, “On shape from shading,” CVGIP, 44, 139-154    (1988).-   7. L. Zhang, B. Curless and S. M. Seitz, “Rapid shape acquisition    using color structured light and multi pass dynamic programming,”    1st International Symposium on 3D data processing visualization and    transmission (3DPVT), July 2002, Padova, Italy.-   8. P. Besl, “Active optical range imaging sensors,” Machine vision    and applications, 1, 127-152 (1988).-   9. E. Horn and N. Kiryati, “Toward optimal structured light    patterns,” Proc. Int. Conf. On Recent advances in 3-D Digital    Imaging and Modeling, 28-37, Ottawa Canada, May 1997.-   10. M. Asada, H. Ichikawa, S. Tjuji, “Determining of Surface    Properties by Projecting a Stripe Pattern,” IEEE Proc. of ICPR, 86    (1986).-   11. M. Asada, H. Ichikawa, S. Tsuji “Determining Surface Orientation    by Projecting a Stripe Pattern,” IEEE Transact. on PAMI, vol. 10,    no. 5 (1988).-   12. S. Winkelbach and F. M. Wahl “Shape from Single Stripe Pattern    Illumination,” Luc Van Gool (Editor), (DAGM 2002) Pattern    Recognition, Lecture Notes in Computer Science 2449, Springer 2002,    page 240-247.-   13. T. P. Koninckx and L. Van Gool “Efficient, Active 3D    Acquisition, Based on a Pattern-Specific Snake,” Luc Van Gool    (Editor), (DAGM 2002) Pattern Recognition, Lecture Notes in Computer    Science 2449, Springer 2002, page 557-565.-   14. R. Kimmel, N. Kiryati, and A. M. Bruckstein, “Analyzing and    synthesizing images by evolving curves with the Osher-Sethian    method,” International Journal of Computer Vision, 24(1), 37-56    (1997); G. Zigelman, R. Kimmel, and N. Kiryati, “Texure mapping    using surface flattening via multi-dimensional scaling,” IEEE Trans.    on Visualization and Computer Graphics, 8 (2), 198-207 (2002).-   15. J. C. Dainty, Laser Speckle and Related Phenomena, 2^(nd) ed.    (Springer-Verlag, Berlin, 1989).-   16. D. Mendlovic, Z. Zalevsky, I. Kiryuschev and G. Lebreton,    “Composite harmonic filters for scale, projection and shift    invariant pattern recognition,” Appl. Opt. 34, 310-316 (1995).

BACKGROUND OF THE INVENTION

The object reconstruction is typically based on estimating the 3-Dtexture of an object (i.e., 3-D map). Various techniques have beendeveloped in this field.

One of the approaches deals with triangulation [1] utilizing two camerasobserving the same object. A relative shift of the same items in theimages acquired by the cameras, respectively, is related to a distanceto these items. This technique is similar to 3-D estimation in humanvision system. The main disadvantage of this approach is its low 3-Dresolution, which strongly depends on a number of pixels in bothcameras, the detail (e.g. texture) present on the scene, and a relativeorientation of the cameras (angle and distance between them). Moreover,this approach does not provide for real-time mapping of objects becausethe extraction of 3-D information requires high level processingoperations such as classification and registration. An additionalproblem with this approach is that 3D information obtained usuallycontains only relatively sparse samples of object depth.

Another known technique of the kind specified utilizes numericalalgorithms based on the use of shadows of edges in the single capturedimage in order to compute the 3-D map of an object [2-6]. Thistechnique, however, requires high level processing, and is inaccuratesince the shadow of edges is the noisiest region of the image.Furthermore, this approach accumulates errors, since the first shadow issued as a reference for the computation in the entire image.

Yet another approach for 3-D estimation is based on projection ofpatterns. Some techniques based on this approach utilize projection of aline onto an object and scanning the object with this line. A curvaturegenerated in the line image is indicative of the 3-D map of the object.This technique, however, does not provide a real time process of theobject reconstruction; it takes time to scan the object with the line;and the estimation becomes more distorted in case the object moves.

Some other techniques of this type utilize projection of special codes[7-9]. The code variation in an acquired image allows for computing the3-D map of the object. These techniques are also not real-time sinceseveral projections are required. In addition, in order to obtain good3-D resolution very large and complicated codes are required; this makesa projection system very expensive and not practical.

Yet other techniques based on the projection of patterns include singleprojection of a 2-D periodic pattern [10-14]. In this case, 3-D detailsof the object shift the lines of the periodic pattern in the capturedimage. A relative shift of these lines is related to the 3-D informationof the object. Although with these techniques scanning is not requiredand the 3-D information can be obtained in real time, these techniquesuffer from the fact that 3-D information is wrapped since relativemovements larger than the period of the projected pattern cannot bedistinguished, and thus one cannot identify whether the obtained shiftis that to be taken as is or an integer multiplied by the period size isto be added. Another disadvantage of this approach is associated withthe depth of focus of the projected pattern. After a certain distance,the pattern is defocused, and it is very hard to extract numerically therelative shift of the periods.

SUMMARY OF THE INVENTION

There is accordingly a need in the art to facilitate the objectreconstruction, by providing a novel technique allowing a real-time andvery accurate mapping of 3-D objects, which can be achieved with a verysimple and inexpensive optical set up.

The present invention provides such a mapping technique, which canadvantageously be used to provide data input to a Man Machine Interface,e.g., for gaming, fitness, etc.; 3D capability for bio-medicalapplications (such as endoscopy), cameras in cellular devices, rangeestimation between vehicles and proximity alarm, intrusion alarm, etc.

Here, the term “object reconstruction” refers to the acquisition of the3-D information of any part or whole of the object outer surfaces,possibly including construction of a 3-D object model (including theobject shape model), from an image, range or other sensed data; the term“real-time” refers to an operation for which the combined reaction- andoperation-time of a task is shorter than the maximum delay that isallowed, in view of circumstances outside the operation.

The terms camera, imaging unit, and imaging device are usedinterchangeably, all referring to the same function of detecting lightand generating image data indicative thereof. The terms projector,projecting system and illumination unit are also used interchangeably.

The main idea of the present invention consists of utilizing projectionof a laser random speckle pattern onto an object the 3D surface data ofwhich is to be reconstructed. Laser speckles are random self-generatedpatterns [15]. Preferably, the pattern is constant, but generally may bepartitioned or other type varying along the Z axis (i.e. along the axisof speckle propagation). The term “constant speckle pattern” used hereinsignifies that the pattern is substantially not varying along the Z-axiswithin the region in which 3D measurements are to be taken. In addition,the depth of focus of such pattern is relatively large, e.g., order ofseveral meters, or as required by a specific application, beingcontrolled by changing the laser spot size on the diffuser and the laserwavelength. Hence, the use of a laser random pattern provides a largelongitudinal range which can be mapped, and allows for significantlyreducing both the optical complexity in designing a projection systemand that of the post-processing, thus allowing for the real-time objectreconstruction.

Generally, in optical systems, a speckle pattern is a field-intensitypattern produced by the mutual local interference of partially coherentbeams.

According to the invented approach, the 3-D map of an object isestimated by examining a relative shift of a laser random pattern(code). This pattern is not periodic, and thus the wrapping problem doesnot exist, thus allowing for both the determination of a range from areference plane and the 3-D mapping of the object. Since the laserpattern is less dependent on defocusing, 3-D information can be obtainedover a large volume.

An optical set up (projection module) can be very simple and cheap: itcan include only a small coherent light source (laser) and a patterngenerator in the form of a light diffuser (e.g., piece of ground glassthat diffuses light impinging thereon by addition of random phase), ore.g. in the form of a holographically recorded, randomized surfacerelief structure, which is accommodated in the optical path of laserlight and scatters this light in the form of constant and random specklepattern onto the object. It is important to note that the inventionallows for acquiring only a single image of the object with a projectedrandom pattern (the so-called single-snapshot solution) and for using asimple image matching algorithm, e.g. a correlation based imageprocessing algorithm, which is thus of low computational complexity.Also, it is important to note that the invention, even when utilizingmore than one images, allows for operation with a single stationarymounted camera (generally, with the single field of view). Theseproperties allow real time realization of the 3-D mapping.

It should be understood that according to the invention the so-called“primary speckles” are considered namely those projected onto the objectto be mapped, and not “secondary speckles” which are typically thoseassociated with the surface roughness of the object and/or aperture ofan imaging lens. Accordingly, an imaging lens may be small.

Thus, according to one broad aspect of the invention, there is provideda system for use in the object reconstruction, the system comprising: anilluminating unit comprising a coherent light source and a generator ofa random speckle pattern (e.g. diffuser unit) accommodated in theoptical path of illuminating light propagating from the light sourcetowards an object thus projecting onto the object a coherent randomspeckle pattern; and an imaging unit for detecting a light response ofan illuminated region and generating image data, the image data beingindicative of the object with the projected speckles pattern and thusindicative of a shift of the pattern in the image of the object relativeto a reference image of said pattern, the system thereby enablingreal-time reconstruction of a three-dimensional map of the object.

Preferably, the system includes a control unit configured for storingreference data indicative of a reference image of the speckle pattern.The reference data is preferably indicative of the image of the specklepattern acquired at a reference plane oriented substantially normally tothe optical path of illuminating light propagation and at asubstantially the same distance from the diffuser and the imaging unit.The control unit is preprogrammed for processing and analyzing the imagedata utilizing the reference data for determining correlation betweenthe object and reference images. The control unit may be preprogrammedfor decomposing the data indicative of the image into Mellin and/orlogarithmic decompositions, thereby obtaining the correlation which isinvariant to scaling and projection distortion of the speckle patterns.

The system is configured to define a measured volume formed byintersection between the illuminating light propagation and the lightcollection of the imaging unit such as to provide for imaging the objectdistanced from the diffuser unit a distance larger than a Rayleighdistance. Each point in said measured volume defines an angle ofintersection between the illuminating and collected light propagationpaths. Considering the triangulation technique, this is a certainnon-zero angle selected to provide appropriate accuracy oftriangulation.

Preferably, the system configuration is such that an average specklefeature size, Δx_(cam), on a pixel plane of the imaging unit is at leasttwo pixels.

Preferably, the diffuser unit and the imaging unit are oriented so as toprovide substantially equal distances from the diffuser and the imagingunit to the object. In this case, the average speckle feature size,Δx_(cam), on the pixel plane of the imaging unit can be determined as:

${{\Delta\; x_{cam}} = {\frac{F}{\phi_{D}}\lambda}},$wherein F is the focal length of an imaging lens; φ_(D) is theilluminating spot size on the diffuser; and λ is the wavelength of theilluminating light.

The matching algorithm allows for a predetermined variability in theaverage speckle feature size Δx_(cam), i.e. the control unit ispreprogrammed for processing and analyzing of image portions/images ofdifferent average speckle feature sizes Δx_(cam), while Δx_(cam) iswithin some predetermined limits. Since Δx_(cam) is different forspeckle pattern portions reflected from different portions of the object(the scaling of Δx_(cam) is given by formulas (9a)-(9d) below), theregion in which imaging of the object will lead to meaningful results isdetermined.

Preferably, the diffuser unit and the imaging unit are located one closeto another, within a fraction s (e.g. 20%) of the Rayleigh distance.

Preferably, the system includes an adjustor configured for reducing theillumination brightness variation between different regions of the fieldof view of the imaging unit. Such adjustor may include a diffractiveoptical element. The latter may be incorporated within or attached tothe diffuser, or located in the optical path of illuminating lightpropagating towards the diffuser. The diffractive optical elementoperates together with the diffuser to adjust the brightness within aplane transversal to the optical path of illuminating light propagation.

In some configurations, the adjustor may be controlled to adjustillumination intensity to partially cancel/smooth the effect of themapped objects on the brightness level received at the imaging unit,e.g. the effects being due to differences in reflection coefficient(albedo), distance, and surface properties. Such an adjustor may receiveinputs from the imaging/control unit, and the intensity distribution tobe projected in the plane transversal to the optical path ofilluminating light propagation.

According to another example, the diffractive optical element may beconfigured to enable reduction of the brightness variability along anaxis substantially parallel to the illuminating light propagation. Thediffractive optical element may be a phase only element accommodateddownstream of the diffuser with respect to the illuminating lightpropagation.

The illuminating unit may be configured as a 4-F Fourier Transformer. Inthis case, the light field in the far field will be a convolutionbetween the far field distribution of the initially projected patternand the Fourier Transform of the diffractive optical element,accommodated between two converging lenses. For example, a diffractiveoptical element is used which is configured as a phase only element suchthat its Fourier transform produces an elliptic cross section ofintensity and is accommodated between two converging lenses.

Preferably, the imaging unit includes a single light detector defining astationary field of view.

According to another broad aspect of the invention, there is provided amethod for use in real-time reconstruction of an object, the methodcomprising: projecting onto the object a random speckle pattern formedby illuminating coherent light; detecting a light response from theobject and generating image data of the object with the projectedspeckles pattern; processing the image data to determine a shift of thepattern in the image of the object relative to a reference image of saidpattern, thereby determining a three-dimensional map of the object.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carriedout in practice, preferred embodiments will now be described, by way ofnon-limiting examples only, with reference to the accompanying drawings,in which:

FIG. 1 is a schematic illustration of an example of an optical system ofthe present invention for reconstructing 3-D objects;

FIG. 2 is a flow diagram of the main steps in a method of the presentinvention;

FIGS. 3A and 3B show the experimental results: FIG. 3A shows a referenceimage (e.g., the projected speckles pattern), and FIG. 3B shows the 3-Dreconstruction;

FIGS. 4A to 4J show some more experimental results: FIGS. 4A-4Billustrate projection and mapping of a hand, FIGS. 4C-4D illustrateprojection and mapping of a tilted plane, FIGS. 4E-4G show projectionand mapping of a basket ball, and FIGS. 4H-4J show projection andmapping of an elephant toy;

FIGS. 5, 6A-6B and 7 schematically illustrate various examples of asystem of the invention utilizing a brightness adjustor.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Referring to FIG. 1, there is schematically illustrated an example of asystem 10 of the present invention for use in 3-D mapping of objects.System 10 is an optical mapping system including an illuminating unit 12configured to project a random speckle pattern (preferably constantpattern) onto an object 13; and an imaging device 14.

Illuminating unit 12 includes a coherent light source 12A, and agenerator 12B of a constant random speckle pattern accommodated in theoptical path of illuminating light, preferably very close (e.g., up to aphysical contact) to the light source output. Light source 12A may beconstituted by a light emitting assembly (laser) and/or by a lightguiding arrangement (e.g., optical fiber) associated with a remote lightemitting assembly. Pattern generator 12B is a light diffuser, forexample a ground glass.

Imaging device 14 includes alight detector 14A (a pixel matrix, e.g.,CCD) equipped with an imaging lens arrangement 14B. The latter may be anintegral part of the light detector or a separate unit in front of thedetector. Preferably, light reflection from the object is detected.

A control system 16, which may or may not be a constructional part ofsystem 10, is provided being connectable (via wires or wireless signaltransmission) to the output of the imaging device. Control system 16 istypically a computer system having inter alia a memory utility 16A, adata processing and analyzing utility 16B, and an input/output utility16C (e.g. a data presentation utility, such as a display).

The device of the present invention may be associated with or include amobile phone device. For example, the imaging unit may be incorporatedin the mobile phone or its output may be connectable to the mobile phoneor other portable computer device. Also, the invention provides forusing the 3D capability for range estimation between vehicles andproximity alarm, as well as for intrusion alarm.

As indicated above, speckles are random patterns generated due to localinterference of scattered light. The brighter spots are positioned wherelight was scattered in phase, and the dark positions are where light wasin anti phase. According to the embodiment of the invention, theprojected speckle pattern is constant in the Z direction (axial axis,passing through the object), that is the pattern does not vary along theZ-axis. It should, however, be understood that the pattern scale doesvary along the Z-axis, namely images of the pattern taken at differentimage planes would be of different scales. An illuminated 3-D objectperforms a shift of the features of a random pattern in the transversalplane (detection plane). Since the pattern is very random, no wrappingproblem exists.

Reference is made to FIG. 2 illustrating the main steps in the method ofthe present invention.

Reference data indicative of the image of a speckle pattern (i.e., imageof the pattern with no object) is provided and stored in the memoryutility of control system 16 (step I). To this end, the speckle patternmay be projected onto a certain region (where an object to be mappedwill then be placed) and the reference image of the speckle pattern isacquired. This reference image may be captured only once.

An image of the object (single image), while located in said region, isacquired (step II) and measured data indicative thereof is generated(step III). To this end, the object is illuminated by light carrying thespeckle pattern, and a light response (reflection) from the object iscollected by the imaging lens and detected by the light detector. Itshould be noted that the present invention provides for operating withthe single image data, thus significantly reducing the complexity ofimage processing to reconstruct the 3-D map of an object.

The measured data is processed using the reference data (step IV) todetermine a relative shift of the features of the random pattern in theimage of the object relative to the pattern in the reference image (stepV). This is implemented using a suitable matching (e.g. correlation)algorithm. The latter can be based on a small moving window scanning thecaptured image and correlating it to the reference image. Thecorrelation peak indicates the relative shift which is related to the3-D information.

The correlation computation has relatively low complexity and may forexample be based on the Fast Fourier Transform (FFT). In addition, sincethe projected pattern is scaled proportionally to a distance between theprojector (laser) and the object, the correlation should be scale andprojection invariant. This can be obtained using harmonic decompositionand/or a proper coordinate transformation applied over the referenceimage before starting correlation [16].

An important parameter is the transversal speckle size (i.e. an averagespeckle size in the transversal plane):

$\begin{matrix}{{{\Delta\; x} = {\frac{L}{\phi_{D}}\lambda}},} & (1)\end{matrix}$wherein L is a distance between diffuser 12B and object 13, λ is theilluminating wavelength, and φ_(D) is the illuminated size of thediffuser 12B. The average speckle feature size is one of the factorsdetermining the 3-D resolution. According to equation (1), this size canbe controlled by changing the diameter φ_(D) of the laser spot at thediffuser and/or laser wavelength λ.

An axial size Δz of the speckle pattern is:

$\begin{matrix}{{\Delta\; z} = {\left( \frac{L}{\phi_{D}} \right)^{2}\lambda}} & (2)\end{matrix}$

Matching the speckle transversal shifts relative to the reference planeis easier for objects with faces close to parallel to the transversalplane of the speckle pattern projection (close to normal to the lightpropagation path). Therefore, in a preferred configuration, thetransversal plane of the speckle pattern propagation is projected ontoan object. In other words, the light incidence onto the object ispreferably close to normal (for the majority of illuminated regions.

Generally, two speckle patterns could appear on the CCD: one beingprimary speckle coming from the diffuser (namely that projected on theobject) and the other being secondary speckle formed during the imagingdue to the lens aperture and/or object material roughness. In order toconcentrate in only one primary speckle pattern, the following conditionmay be considered: φ_(L)>>φ_(D), where φ_(L) is the size of the imaginglens.

Control system 16 operates to process the measured data by applyingthereto a numerical algorithmic to extract the 3-D information. Itshould be understood that the algorithm according to the presentinvention, as described here, includes a novel combination of knownmathematical processes. The invention utilizes this algorithm togetherthe unique optical setup, enabling real time 3D mapping.

The algorithm used can have low computational complexity and can allowreal time operation. The following is an example of an algorithmicconstellation suitable to be used as part of the data processing step inthe present invention.

To obtain one specific depth point, a transversal shift of its vicinityfrom the reference pattern needs to be found. One possibleimplementation of this matching is by searching for the correlationpeak, which may be implemented by taking one or more windows from theimage, representing the statistics/neighbourhood of the inspectionpoint, and computing a match, e.g. correlation of such window(s) withthe reference image. The windows can be taken with any amount ofoverlap. For each camera pixel, a depth sample could be thus obtained.The achievable depth (the 3D) resolution (δZ along the Z-axis) varieswith varying Z and depends solely on the optical setup (i.e., relativelocation of the laser and the camera), the speckle properties (featuresof the speckle pattern) and the camera resolution (which is the physicalparameter of the camera).

The algorithmic approaches upon which the 3-D reconstruction may bebased on image matching algorithms, from a very basic exhaustive rastersearch, through a more sophisticated prediction-based region growingmethods, up to a higher level maximum-likelihood or other sophisticatedimage matching algorithms. Various approaches differ from each other inmany factors: the more sophisticated approaches have much morecomputational complexity while producing much more accurate and lessnoisy data than the simple ones.

The prediction-based region-growing methods present a good tradeoffbetween a complexity and performance and are based on the followingobservation: two close points on one object are usually characterized bya small height (along Z-axis) difference between them, the so called“object continuity assumption”. Hence, the Z value (depth) of a pointfrom its neighboring points on the same region (object) can beapproximately predicted. The prediction is tested and refined, and incase it is found to be adequate, the point is joined to the givenregion. If the prediction/refinement presents an inadequate match withthe reference, this is indicative of that the Z difference is nonnegligible and thus the point under inspection belongs to a differentregion from its neighboring (“father”) point.

It should also be noted that window(s) for the correlation can be eitherconstant (e.g. 16×16 pixel window), or flowing in accordance with thelocal speckle/edge/object properties.

The following is an example of one possible implementation of aprediction-based region growing algorithm with a constant window size.The algorithm contains the following steps:

1) Relevance/Shadow Preparation Step.

Run over the picture (image of the object) with the resolution step(sampling points equal to M and N multiplied by the resolution, where Mand N are integers) and determine whether the sampling point is a“shadow” to be marked SHADOW, or a relevant speckle window to be markedUNKNOWN. At further stages, the status of each output point ismaintained, while at this first stage some points have status of UNKNOWNand others have status of SHADOW.

2) “Obtain a New Region Anchor” Step.

While the number of UNKNOWN points is more than some pre-definedpercentage of the total output points, a random point is chosen thatcurrently has the status UNKNOWN and a matching to the reference imageis performed, e.g. by correlating the window W_(x)×W_(y) pixels aroundthe chosen point with the reference image.

It should be noted that the window size W_(x)×W_(y) is subject tooptimization, the tradeoffs being on the one hand the “enoughstatistics”/discrimination and on the other hand the complexity andsmall objects smearing. It should also be noted that due to geometricconstraints, with a proper imaging unit/projector system calibration(i.e. when the X axis of the imaging unit is parallel to the lineconnecting the optical center of the imaging lens and the center of thelaser spot on the diffuser), the possible lateral shifts of the specklepattern can be limited to a rectangle which covers a few pixels, up anddown from the current point and about a known fraction of width of thepicture to the right and to the left from the current point (in theexperimental setup shown in FIG. 1 the camera is to the right of thelaser, therefore the speckle shift is to the right if the mapped objectis closer than the reference, and to the left—otherwise).

Additionally, within the above geometric constraints, search is carriedout for a point with a value of normalized correlation higher than acertain threshold. If none of the checked correlations reaches thethreshold, a value of the best correlation is selected to check whetherit passes a lower threshold: if it does, it is assumed that this is theshift of the speckle; and if it doesn't, it is understood thatadditional investigation is needed and the described below step 2a) isperformed aimed at deciding on initiating the new region. If a point forwhich correlation higher than a lower threshold is found, such point iscalled region anchor, and the region growth is attempted around it. Togrow the region, step 3) below is carried out.

2a) Decision to Grow Region.

If the match has failed, the region is further investigated by anattempt to find sufficient evidence for existence/absence of a growableregion at this position. To gather sufficient evidence, region growingstep (3) is attempted, and the grown portion is decided to represent avalid region if either an anchor (a sufficiently strong point) is foundwithin a region or a mass of consistent points are found on the region.In this way, a majority voting is performed to leave the region. In caseno sufficient evidence is obtained, the region is removed and the anchor(first) point is marked as BAD, and step 2) is repeated to find a validanchor point to grow a new region.

3) Region Growing.

The region growing is done using 4-connectivities (left/right/up/down).In the present example, the implementation of region growing is fairlysimple. A FIFO (first in first out) plurality of ACTIVE points is used,where each such point (active point) has already been correlated withthe reference and the correlation proved to be successful. Each time,one point from the FIFO set is fetched and its four neighbors arechecked. For each neighbor which is marked as UNKNOWN, correlations of aW_(x)×W_(y) (e.g. 16×16) window to the reference are determined, whereonly a few possibilities are checked within a small rectangle (e.g. 5points with offsets of (0,0) (−1,0) (1,0) (0,−1) and (0,1)) around thepredicted shift of the speckle. The predicted shift is the shift of itsoriginating ACTIVE point (called “father” class point). If there is agood correlation, the point is marked as ACTIVE and is added to the FIFOset; and if there is no good correlation, the point is marked as EDGE(its height is currently set to be equal to the height of the fatherpoint). When the FIFO is “emptied”, the region edge is marked, and theprocess returns back to step 2) to grow a new region.

4) Region Competition.

Region competition can be implemented to considerably improve quality ofregion edges. One possible way which gives good results and iscomputationally inexpensive is to attempt growing a region not only intothe UNKNOWN point space, but to any point space with depthdiscontinuities, e.g. belonging to a different region. The competitioncriterion is the correlation value, “winner takes all” per pointstrategy has been found to yield good results.

Based on the prediction and quick stop of the correlation procedure upondetecting bad points, the region growing algorithm provides a real-timereliable tool for depth recovery, having an excellent trade-off betweenits complexity and quality.

It is important to note that the larger a distance between theprojection device (illuminating unit) and the projection plane (objectplane), the larger the obtained speckles in the projection plane. On theother hand, the pixel size of the imaging device changes according to adifferent set of rules. Moreover, the speckle pattern is distorted viaprojection on slanted object surfaces. An (algorithmic) method to obtaincorrelation which is invariant to scaling and projection distortion ofthe speckle patterns, involves performing Mellin and logarithmicdecompositions [16] of the reference speckles pattern.

The Mellin decomposition provides scale invariance:

$\begin{matrix}{{{f\left( {r,{\theta;x_{0}},y_{0}} \right)} = {\sum\limits_{N = {- \infty}}^{N = \infty}{{f_{N}\left( {{\theta;x_{0}},y_{0}} \right)}r^{{{\mathbb{i}2\pi}\; N} - 1}}}}{{f_{N}\left( {{\theta;x_{0}},y_{0}} \right)} = {\frac{1}{T}{\int_{r_{0}}^{R}{{f\left( {r,{\theta;x_{0}},y_{0}} \right)}r^{{{- {\mathbb{i}2\pi}}\; N} - 1}r{\mathbb{d}r}}}}}} & (3)\end{matrix}$Here, f(r, θ; x₀, y₀) is the object decomposed around x₀,y₀ coordinates;f_(N) is the Mellin harmonic; N is the harmonic order; r₀ is the minimalradius of the decomposed object; R is its maximal radius; andT=exp(r₀/R). If one harmonic is chosen, the correlation result will bescale invariant.

The logarithmic decomposition is described as follows:

$\begin{matrix}{\mspace{20mu}{{{f\left( {x,y} \right)} = {\frac{1}{2T}{\sum\limits_{N = {- \infty}}^{N = \infty}{{f_{N}(y)}{x}^{{i\; 2\pi\; N} - {1/2}}}}}}{{f_{N}(y)} = {{\int_{- X}^{- x_{0}}{{f\left( {x,y} \right)}\left( {- x} \right)^{{{- i}\; 2\pi\; N} - {1/2}}{\mathbb{d}x}}} + {\int_{x_{0}}^{X}{{f\left( {x,y} \right)}x^{{{- i}\; 2\pi\; N} - {1/2}}{\mathbb{d}x}}}}}}} & (4)\end{matrix}$The object is not zero within the range of |x|>x₀ and |x|<X, andT=exp(x₀/X). Choosing one harmonic provides projection distortioninvariance when correlating.

The speckle size changes due to the projection system and the imagingsystem can also be mutually compensated by means of optical setup. Tounderstand the way this can be achieved, let us now elaborate on thedetails of the speckle pattern scaling.

When the illuminating beam is modeled as a Gaussian beam, thediffraction formula gives the following dependence of the beam radiusW(z) on distance Z:

$\begin{matrix}{{{W(z)} = {{W_{0}\sqrt{1 + \frac{Z^{2}}{Z_{R\;}^{2}}}} \approx {W_{0}\frac{Z}{Z_{R}}}}},{z_{R} = {\frac{\pi\; W_{0}^{2}}{\lambda}.}}} & (5)\end{matrix}$In (5), λ is the beam wavelength, W₀ is the radius of the beam waist(equal to φ_(D)/2—half of the diameter of the beam illuminating thediffuser), and Z_(R) is the Rayleigh distance. In the approximation of(5) it is assumed that Z>>Z_(R).

It should be noted that a Rayleigh distance is also the distance atwhich the far field approximation is valid since then the quadraticphase factor in corresponding Fresnel integral is smaller than one.

It should also be noted that with the technique of the presentinvention, the object is preferably located at a distance L from thediffuser higher than the Rayleigh distance. It should be noted that ateach Rayleigh distance from the beam waist, the beam area doubles (fordiffraction-limited beams, this distance is determined by the waistradius, the refractive index, and the wavelength in the material, forimaging in the air the refractive index is approximately that of freespace, i.e. 1.0).

The light intensity I at camera 14 depends on L (a distance betweenprojector (illuminator) 12 and object 13) and on d (a distance betweenobject 13 and camera 14), as 1/L²d²:

$\begin{matrix}{\left. I \right.\sim\frac{1}{L^{2}d^{2}}} & (6)\end{matrix}$The 1/L² part of the dependence (6) is due to the divergence of theprojected beam carrying the speckle pattern.

It should be noted that the Gaussian beam model refers to the beam as awhole. The light beam radius W(z) increases proportional to Z, and theintensity density reduces as 1/Z². As a result, the intensity of lightimpinging on the object is proportional to 1/L². The 1/d² part of thedependence (6) is due to the divergence of the coherent beam reflectedfrom the object towards the camera.

On the other hand, a smaller portion of the speckle pattern is projectedon the object (or object portion) when the object is further from thelight source unit. The number of the speckle dark and light spots(speckle pattern features) falling into an interval defined by theobject size is determined by the ratio of the object size s to theaverage speckle size Δx of (1):

$\begin{matrix}{\left. N \right.\sim\left. \frac{s}{\Delta\; x} \right.\sim\frac{s}{L}} & (7)\end{matrix}$

When light from the object is reflected onto the light detector, itforms there a spot of size s_(LD) (i.e. s_(LD) is the size of the objectprojection onto the photodetector plane):

$\begin{matrix}{s_{LD} = {\frac{F}{d}s}} & (8)\end{matrix}$Here F is the focal distance of the collecting (imaging) lens.

The average feature size projected on the photodetector is determined byratio of (8) to (7):

$\begin{matrix}{{\left. \frac{s_{LD}}{N} \right.\sim\frac{F}{d}}L} & (9)\end{matrix}$

In a preferred configuration, the diffuser plane and the detection plane(more exactly, the plane of imaging lens 14B) are located such as toprovide for substantially equal L and d (the distances between thediffuser and the object and between the camera and the object).

On the other hand, the optical setup is configured so as to ensure acertain non-zero angle α between the axes of propagation of illuminatinglight incident onto the main object plane and that of light returnedfrom there to the light detector, so as to enable triangulation basedcalculations. The accuracy of the 3D reconstruction will be

${\delta\; Z} = {\delta\; x_{LD}\frac{d}{F}\frac{1}{\tan\;\alpha}}$(δZ is the 3D resolution, and δx_(LD) is the resolution of the shift inthe pixel plane obtainable by the correlation algorithm, e.g. the pixelof the camera). The angle α is approximately equal to L′/L, where L′ isthe distance between the projector and the camera.

In the experimental setup used by the inventors, the mapping system hadthe following parameters: L′=20 cm, L≈2 m, δx_(LD)=6 microns, and F=8mm; thus δZ=15 mm. It is seen from the above, that the distance L′between the projector and the camera can be preselected so as to enablethe mapping system to operate with a desired resolution, e.g. a fewmillimeters.

As indicated above, practically, the diffuser plane and the plane oflens 14B are located such as to provide for substantially equal L and d(the distances between the diffuser and the object and between thecamera and the object). In order to take into account both of suchrequirements as L=d and a minimal distance L′ from the projector to theimaging unit, a change of the speckle size on the imaging unit (camera)with changes of L and d should be considered.

The size of the speckle on the camera plane for the case that L is notequal to d is:

$\begin{matrix}{{\Delta\; x_{cam}} = {\frac{\lambda\; F}{\phi_{D}} \cdot \frac{L}{d}}} & \left( {9a} \right)\end{matrix}$In a preferred configuration, the size of the speckle on the cameraplane is the same for the speckles reflected from various parts ofobject. The scaling of the visible speckle dimensions (i.e. on thecamera plane) is suppressed if L=d. The latter condition could beguaranteed for almost the entire 3D space by placing diffuser and cameralens very close one to another, however in practice, there is a certaindistance L′ between the camera and the projector.

Considering that L and d are different on a fraction of the Rayleighdistance Z_(R):|L−d|≦εZ _(R).  (9b),the size of the speckle scales with d:

$\begin{matrix}{{\Delta\;{x_{cam}(d)}} \approx {\frac{\lambda\; F}{\phi_{D}}\left( {1 + {ɛ \cdot \frac{Z_{R}}{d}}} \right)} \approx {\frac{\lambda\; F}{\phi_{D}} + {ɛ \cdot \frac{\phi_{D}F}{d}}}} & \left( {9c} \right)\end{matrix}$The matching algorithm used allows for some maximal scaling factor γ,connected to the maximal allowed visible speckle size

Δ x_(cam)^(ma x):

${\Delta\; x_{cam}^{{ma}\; x}} = {\frac{\lambda\; F}{\phi_{D}} \cdot {\left( {1 + \gamma} \right).}}$Hence, the difference between L and d, and consequently ε and L′, arelimited:

$\begin{matrix}\left. {ɛ \leq {\frac{d}{\phi_{D}} \cdot \gamma}}\Rightarrow{L^{\prime} \leq {ɛ \cdot Z_{R}} \leq {\frac{d}{\phi_{d}} \cdot \gamma \cdot {Z_{R}.}}} \right. & \left( {9d} \right)\end{matrix}$

As it follows from the equations (9a)-(9d), the fact that L is close tod, or, L′ is bounded by equation (9d) for a given γ, will provide forthe scale (average feature size) differing by at most factor of 1+γ overdifferent portions of the speckle recorded on the imaging device. Thesespeckle pattern portions might be reflected from objects at differentpositions relative to the imaging device, projected on the differentregions of a 3D object surface or on differently distanced objects; inany case, the images of these portions will have substantially the samefeature size (up to a factor of 1+γ) when measured in pixels of thephotodetector. This average feature size will be thus substantiallyequal to the feature size of the reference image.

Thus, correlating an object image and a reference image using windows ofthe same size in both of these images is justified, since correlation asany matching operation is inherently robust towards certain distortions,depending on the speckle feature size, some amount of scaling includedin this robustness. The specific parameter γ that is allowed is easilydetermined by any person of ordinary skill, given the specific setupparameters and the pattern properties, by considering the matchingcriterion over the scaled by (1+γ) and the non-scaled version of thepattern.

The correlation allows for determining shifts of the speckle patternportions which are due to the differences between the 3D topography ofan object and that of the (flat) reference plate (producing the specklereference pattern).

The required proximity of L and d can be enabled by placing the diffuserunit and the imaging unit of the system at a distance from each otherequal to a fraction ε (e.g. 0.5) of the Rayleigh distance of theilluminating light. The above described matching of the optical setupenables to obtain a scale invariance without the need to reside to othermeans, e.g. Mellin transform. It should be noted that speckles impingingon slanted surfaces undergo distortions mostly in the form ofprojections. Since the projection of the speckle in the preferredconfiguration of the optical setup is such as to ensure the maximallyclose to normal light incidence on the main object plane, and since thespeckle pattern is inherently capable of withstanding a certain amountof distortion, in the preferred configuration there is no need to resideto other means, e.g. logarithmic transform.

In another preferred configuration, diffuser 12B, lens 14B and lightdetector 14A are configured to provide an average feature size of theimaged speckle pattern that matches the required resolution. With noneed to reside to special means, the average speckle feature size ispreferably of about 2 pixels. It should be understood that the averagespeckle feature size, Δx_(cam), on the camera is determined by eq. (1)and (8) above, where s in eq. (8) would be Δx of eq. (1):

$\begin{matrix}{{{\Delta\; x_{cam}} = {{\frac{F}{d} \cdot \frac{L}{\phi_{D}}}\lambda}},{{{or}\mspace{14mu}{considering}\mspace{14mu}{that}\mspace{14mu} L} \approx d},{{\Delta\; x_{cam}} = {\frac{F}{\phi_{D}}\lambda}}} & (10)\end{matrix}$Such imaging setup allows for obtaining the highest resolution, becausemaximum information is contained in the each pixel signal.

It should also be noted that the optical setup of the present inventionallows for a large range of distances to the object. The minimalpossible distance is the Rayleigh distance (e.g. 0.5 m in a specific butnot limiting example used by inventors), and the maximal distance isdetermined by the object size and the speckle size at the object. Thenumber of speckles projected onto the object should not be much lessthan the size of a correlation window divided by the average specklefeature size in pixels.

One of the properties inherent to the laser speckle is that itsprojection on an object yields highly contrast images. This is because alaser speckle pattern is created with high contrast, and, since laserspeckle pattern propagates by way of self-regeneration, this highcontrast is maintained through the depth of focus of the laser specklepattern. High contrast images can be represented by intensities of lighttaking values 0 or 1 for each pixel, or this high contrast can beutilized in some other way. Thus, the high contrast property of a laserspeckle pattern allows for reduction of processed data and faster imagereconstruction.

It should also be noted that, as seen from the equation (2), eventuallythe speckle pattern is varied along the Z direction (the longitudinalaxis). Thus, with the constant random reference pattern (diffuser), aset of reference images may be taken at different locations of theprojection plane relative to the projection device (these images willthus be different in accordance with the longitudinal variation of thespeckle pattern), and 3-D correlation may then be performed. In thiscase, the obtained approach allows infinite 3-D mapping range.

Reference is now made to FIGS. 3A-3B and FIGS. 4A to 4J showing severalexperimental results that verify the advantageous features of theinvention. In these experiments, the image reconstruction was performedin real time at video rate using the set up of FIG. 1.

FIGS. 3A-3B exemplify reconstruction the image of a coffee cap. Theilluminating unit (12 in FIG. 1) utilized a green Nd:YAG laser as thelight source 12A and a piece of ground glass (diffuser) 12B to projectthe constant random speckles pattern. The control system waspreprogrammed with a correlation algorithm utilizing a sliding window of16×16 pixels. FIG. 3A presents a reference image (e.g., the projectedspeckles pattern with no object), and FIG. 3B shows a mesh of theobtained 3-D reconstruction.

FIGS. 4A-4B exemplify 3-D mapping of a hand. FIG. 4A shows the hand withthe projected speckle pattern; and FIG. 3B shows the 3-D reconstruction.

FIGS. 4C-4D illustrate the projection and mapping of a tilted plane:FIG. 4C is the plane image with the projected speckles pattern and FIG.4D is the 3-D reconstruction. FIGS. 4E-4G show the 3-D mapping of abasket ball, where FIG. 4E is the image of a ball, FIG. 4F is the ballwith the projected speckles pattern, and FIG. 4G is the 3-Dreconstruction. FIGS. 4H-4J show the projection and mapping of anelephant toy: FIG. 4H is the image of the toy, FIG. 4I is the toy withthe projected speckles pattern, and FIG. 4J is the 3-D reconstruction.It should be noted that different colors of the displayed reconstructionindicate the 3-D obtained information.

The present invention thus provides a novel method and system for 3-Dmapping, in which a random speckles pattern is used to map the 3-Dinformation of objects and to estimate the ranges to the certainreference plane. This technique allows for extracting highly resolvedand real-time 3-D information. The 3-D information is obtained byextracting the local relative transversal shift of the random pattern inthe captured image in comparison to the reference image. This techniquehas low computational complexity, and has no wrapping problems asexhibited in other techniques using periodic patterns projection. Theoptical system used is very simple.

It should be noted that the present invention is capable of improvingthe brightness of light detection. In this connection, the followingshould be noted.

Brightness level is different for objects and/or object portions beingat different distances from the light source and/or the light detector.Each pixel of the light detector array acquires light from a spot ofdiameter Δx_(Z):

$\begin{matrix}{{{\Delta\; x_{Z}} = {\frac{d}{F}\delta\; x}},} & (11)\end{matrix}$where δx is the pixel size.

The brightness of the detected speckle pattern is determined by theintensity of a signal reaching a single pixel of the light detector:

$\begin{matrix}{{\left. I_{P} \right.\sim I} \cdot \frac{\Delta\; x_{Z}^{2}}{s^{2}} \cdot {\left. \frac{D^{2}}{d^{2}} \right.\sim\frac{1}{L^{2}}}} & (12)\end{matrix}$where D is the diameter of the imaging lens and it is related to thespherical angle in Str, at which the radiation is reflected from theobject.

As can be seen from eq. 12, the brightness level received at thedetector is proportional to 1/L², therefore close object regions and farobject regions will be seen by the detector with different brightnesslevels, depending on the distance, thus affecting the 3D-reconstructionperformance. An additional factor is the reflection coefficient (albedo)difference between different regions of the object.

The control system can identify light spots in the speckle pattern bycomparing their brightness levels with a predetermined threshold.However, such an algorithm will identify more light spots for objects(or object portions) situated closer to the light source. Also, thelight spots will have larger areas and also different shapes for objectssituated closer to the light source. On one hand, this effect can beutilized for 3D-reconstruction and range determination. On the otherhand, this effect is preferably taken into account during or prior tothe correlation procedure.

Referring to FIG. 5, there is shown, by way of a block diagram, anotherexample of a mapping system 60 of the invention. To facilitateunderstanding, the same reference numbers are used for identifyingcomponents that are common in all the examples of the invention. System60 includes an illuminating unit 12 configured for projecting a laserrandom speckle pattern onto an object 13, an imaging device 14, and abrightness controller (adjustor) 25. The latter is configured forcontrolling the variation of the brightness in the field of view of thecamera or perceivance of this variation by the system. Adjustor 25constitutes a mechanism of increasing the mappable range. It should beunderstood, that more than one adjustor may be used in the mappingsystem.

In the example of FIG. 5, adjustor 25 is implemented as a sub-utilitywithin the data processing and analyzing utility 16B of the controlunit. Such a sub-utility may perform the above described Mellintransformation.

In some embodiments, brightness adjustor 25 is configured for reducingthe illumination brightness variation between different regions of thefield of view of the camera and can be implemented as an optical unitarranged to be anywhere in the light propagation path. For example, theadjustor can be implemented as an optical unit and may be integratedwith light source unit 12A or diffuser 12B, or can be a separate unitarranged in the illumination path downstream of diffuser 12B, or inbetween light source unit 12A and diffuser 12B.

Likewise, adjustor 25 can be implemented as an analog processing unitlocated between the light detector and the control unit, or being a partof light detector 14A or a part of control system 16. In one example thebrightness level is controlled by local adjustment of automatic gaincontrol (AGC), i.e. by control of the amplification of the analogreadout at each pixel or group of pixels. This allows for receivingdigital images having more uniform brightness level; thus allowing forextending the mappable range with the light detector having a certainfixed dynamic range.

Adjustor 25 is configured for controlling the brightness level (being anoptical processor or a digital processor) or controlling therepresentation of the brightness level (being associated with thedetector output). For example, adjustor 25, configured as an opticalprocessor, can perform an optical coordinate transformation prior to thedigital sampling. Such an optical coordinate transformation may containa step of transforming the Cartesian (x,y) coordinates into polar-like(log r, θ) coordinates by using the Saddle point integration techniqueor multi facet approaches [e.g. Zeev Zalevsky, David Mendlovic “Opticalimplementation of the Bode transform”, Applied Optics, Vol. 34, Issue 5,pp. 828-(February 1995)].

The following are some specific but not limiting examples of the opticalmapping system configured and operable according to the invention.

FIG. 6A exemplifies a mapping system 80 in which a diffractive element12D is accommodated in the optical path of speckle pattern propagatingtowards the object. Diffractive optical element can be configured as anadjustor 25 implementing reduction of contrast (relative brightness) forplanes differently distanced from the light source. In the presentexample, adjustor 25 is incorporated in or attached to the diffuser.Adjustor 25 is configured to produce a non diffractive beam (in thelongitudinal range) of a decreased beam divergence. This may beimplemented e.g. by combining special semi random diffractive opticalelement having random distribution along the radial axis and symmetryalong the angular axis (having rings structure) and an Axicon (notshown) attached thereto which is a cone like element providing extendeddepth of focus for random pattern generators. It should be noted, thateven without the Axicon such a ring based diffuser can extend the depthof focusing.

FIG. 6B schematically shows the operational principles of such acone-like diffractive element 25. Element 25 is located close to adiffuser 12B (e.g. attached to the diffuser), and is configured andoperable for producing the non-diffractive beam for the beam spot, whileallowing the speckles appearance inside the spot. As a result of thelight passage through element 25, three different successive regions arecreated: a light propagation region R₁ being a regular diffractionregion, a light propagation region R₂ being the volume of interest wherethe target may appear, and a light propagation region R₃ being again aregion where the regular diffraction is obtained. Considering thetypical Axicon operation, since the object is placed in region R₂, thereflected light will fulfill the regular diffraction laws as appears inregion R₃. The cross section can be considered similar to two prismsattached back to back; hence, the beams illuminating the cross-sectionalregion are redirected towards the center where interference occurs andnon diffractive beam is formed. Diffractive element 25 provides for asmaller divergence of a laser speckle pattern carrying beam withinregion R₂. Thus, the light intensity will vary slower with a distance Lfrom the light source than that of equation (12) above. This makes thebrightness level less dependent on the distance from the light sourceand thus more uniform.

It should be noted, that in the example of FIG. 6A, diffractive opticalelement 12D can be configured to perform various functions, includingthe brightness adjustment or not. If the diffractive optical element(DOE) is located close (up to a physical contact) to the diffuser, afterthe diffuser in the laser beam optical path, the light field in the farfield will be a convolution between the speckle far field distributionand the Fourier Transform of the DOE. Thus, various functions (e.g.speckle shaping) can be achieved with the optical setup of FIG. 6A.Another approach provides the 3-D mapping resolution allowing separationof segments of Δz along the Z axis. In case the observed object hasvariations along the Z axis which are larger than the mapping resolutionΔz, distortions occur (e.g. for a tilted plane as an object). Thosedistortions occur mainly since the region for the reference search issignificantly shifted aside. The distortions can be identified byshearing distortions of the object. To this end, shaping of the specklescan be used. If for instance the speckles have elliptic shape, thenshearing distortions can be detected according to the variation in theoriginal speckle shape. The diffractive optical element 12D used in thissetup is a phase only element such that its Fourier transform producesfor example an elliptic cross section of intensity (e.g. a tilted line).Such a DOE can for example be designed based on the technique disclosedin the following publication: Z. Zalevsky, D. Mendlovic and R. G.Dorsch, “The Gerchberg-Saxton Algorithm Applied in the FractionalFourier or the Fresnel Domains,” Opt. Let. 21, 842-844 (1996); or otherknown methods can be used.

Reference is made to FIG. 7, showing another example of a projectionmodule 90 suitable to be used in a mapping system of the invention.Setup 90 includes a laser source 12A, a diffuser 12B, a first converginglens 12C, a diffractive optical element 12D, and a second converginglens 12E. The elements are arranged as the so-called “4-F FourierTransformer”: diffuser 12B is in the back focal plane of lens 12C,diffraction element 12D is in the front focal plane of lens 12C and inthe back focal plane of lens 12E, and the focal lengths of the lensesare equal. Lens 12C applies the Fourier transform of the speckle patterngenerated by diffuser 12B; at the diffraction element, its transmissionfunction is multiplied with the Fourier transform of the specklepattern; and lens 12E produces the inverse Fourier of the productfunction resulting from multiplication. Thus, in the far fieldapproximation (Z is larger than the Rayleigh distance) where the objectis placed, the speckle random distribution is multiplied with theelement 12D.

In one example, element 12D can be implemented as an intensityequalization mask: an amplitude mask, which transparency function isselected so as to provide a predetermined light intensity in the farfield. For example, element 12D can be a mask that is more transparentat its periphery regions than in its center. The projected light will bedetermined by the mask transparency and the speckle pattern. This way,the light intensity distribution can be made significantly more uniformin the transversal plane. To summarize, this element can contribute inthe equalizing of the energetic distribution of the projected specklepattern

Thus, the present invention provides an effective 3-D objectreconstruction technique using a simple and cheap optical setup based onthe principles of triangulation. The invention can use only a singleimage; can operate with the single stationary mounted camera; and allowsfor a large range of possible distances to an object.

The invention claimed is:
 1. A system for object reconstruction,comprising: an illuminating unit, comprising a coherent light source anda generator of a non-periodic pattern comprising a diffractive opticalelement (DOE) in an optical path of illuminating light propagating fromthe light source toward an object, thereby projecting the non-periodicpattern onto an object; an imaging unit configured to detect a lightresponse of an illuminated region and generating image data indicativeof the object within the projected pattern; and a processor, configuredto reconstruct a three-dimensional (3D) map of the object responsivelyto a shift of the pattern in the image data relative to a referenceimage of the pattern.
 2. The system according to claim 1, wherein thereference image is acquired at a reference plane oriented normally tothe optical path of the illuminating light.
 3. The system according toclaim 2, wherein the reference plane is at the same distance from thegenerator of the non-periodic pattern and from the imaging unit.
 4. Thesystem according to claim 1, wherein the processor is configured toreconstruct the 3D map by determining a correlation between the imagedata and the reference image.
 5. The system according to claim 1,wherein the DOE is configured to adjust a brightness variation of theprojected pattern between different regions in a field of view of theimaging unit.
 6. The system according to claim 1, wherein the projectedpattern comprises a Fourier transform of the DOE.
 7. The systemaccording to claim 1, wherein the imaging unit comprises a single lightdetector having a stationary field of view.
 8. A method for objectreconstruction, comprising: projecting onto an object a non-periodicpattern formed by a coherent light source and a generator of thenon-periodic pattern comprising a diffractive optical element (DOE) inan optical path of illuminating light propagating from the light sourcetoward the object; detecting a light response of an illuminated regionand generating image data indicative of the object within the projectedpattern; and processing the image data so as to reconstruct athree-dimensional (3D) map of the object responsively to a shift of thepattern in the image data relative to a reference image of the pattern.9. The method according to claim 8, wherein the reference image isacquired at a reference plane oriented normally to the optical path ofthe illuminating light.
 10. The method according to claim 9, wherein thereference plane is at the same distance from the generator of thenon-periodic pattern and from an imaging unit that detects the lightresponse.
 11. The method according to claim 8, wherein processing theimage data comprises reconstructing the 3D map by determining acorrelation between the image data and the reference image.
 12. Themethod according to claim 8, wherein the DOE is configured to adjust abrightness variation of the projected pattern between different regionsin a field of view of the imaging unit.
 13. The method according toclaim 8, wherein the projected pattern comprises a Fourier transform ofthe DOE.
 14. The method according to claim 8, wherein detecting thelight response comprises capturing an image using a single lightdetector having a stationary field of view.